Trinity chief executive Michael Carter revealed at the start of the week that he has made an offer to Cronulla for the 31-year-old front rower, whose twin brother David is already on the books at Belle Vue.
The Sharks’ 2016 premiership match-winner, whose defection from Australia helped lift Tonga to number four in the world, has 18 months left on his contract with the Sydney club but is currently out of favour.
“It’s huge for the club that we’re able to be in the market to sign such a quality player from the NRL,” Wakefield coach Chester said at his weekly press conference.
“He’s been there and done that. He’s a State of Origin player and has played for his country. He’s also played for Tonga and wants to play in the World Cup at the end of the year.
“He’s obviously not been getting that game time and Woolfy (Tonga coach Kristian Woolf) has made it clear that he needs to play.
“Hopefully, he gets that game time. Whether that be over there or whether that’s here, we’ll know within three or four weeks.”
Wakefield freed up space on their overseas quota by offloading Adam Tangata to Halifax and Chester says he spoke to Sharks head of football Darren Mooney on Wednesday about the prospect of signing Fifita.
“We’ve had a couple of discussions over the last couple of days,” Chester said.
“He’s serving a three-week ban so I don’t envisage anything getting done in the short term. I don’t think the fact their coach has left has helped.
“We’ll have to see how it unfolds. There’s a lot of things to take into consideration – he’s got three kids that are all in school.
“We’re a million miles off at the minute. If it happens, then great, if not we’ll look elsewhere. The budget is there and so is cap space to bring in someone else.
“It would be a big boost to the fans and the club and it would bring the best out in Dave. He will add some great value to this club, both on the field and off it.
“We saw the impact that Dave Fifita had when he came over in 2016 and his brother will have a very similar impact.”
Andrew Fifita, who has made 10 Origin appearances for New South Wales and won 17 caps for Australia and Tonga, has been plying his trade with feeder club Newtown Jets, although he picked up a three-match ban following his most recent match at the weekend.
The twins played together at Cronulla from 2014-16 and for Tonga from 2010.